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siv class="wrticle_-uthor_s" /p/lass="waold"cd="sr29485-16.-uthor_-1>uis T-url=/component/autheor/?dkey"0.1051/0004-6361/201629485"amp;An=1 llass="crthor" >. Buldgen"/span>1/apup>, span>cd="sr29485-16.-uthor_-2>uis T-url=/component/autheor/?dkey"0.1051/0004-6361/201629485"amp;An=2 llass="crthor" >. R. Reese"/span>2/apup>and espan>cd="sr29485-16.-uthor_-3>uis T-url=/component/autheor/?dkey"0.1051/0004-6361/201629485"amp;An=3 llass="crthor" >. A. Dupret"/span>1/apup>/p> /div> dp/lass="waff"1/apup> nstitut d’strophysique et Géphysique de l’niversitéde Lièe, BAllé du 6 Aoû 17, 44000 L Lièe, BAelgium"
e-mail: gbldgen"@tudint/.ulg.ac.be
spup>2/apup>aESIA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Université, UPMC Univ. Paris 06, Univ. Paris Diderot, Sorbonne Paris Cité 5 place Jules Janssen, 992195 M Meudon Cedex, FFrance"
/p> dp/lass="wis tory"class="iaold"<5 August20176
span>class="iaold"<1 Octobero0176

dp/lass="waold" /i>ontext. &hanks to the space-based photometry missions CoRoT and &/i>epler& we now benefit from a wealth of seismic data for stars other than the sun. In the future, K2, Tess, and &/i>lato &ill complement this data and provide observations in addition to those already at hand. The availability of this data leads to questions on how it is feasible to extend kernel-based, linear structural inversion techniques to stars other than the sun. Linked to the inversion problem is the question of the validity of the linear assumption. In this study, we analyse the limitations of this assumption with respect to changes of structural variables.&/sp /i>ims. &e wish to provide a more extended theoretical background to structural linear inversions by doing a study of the validity of the linear assumption for various structural variables. We thus point towards limitations in inversion techniques in the asteroseismic and helioseismic cases.&/sp /i>ethods. &irst, we recall the origins of the linear assumption for structural stellar inversions and explain its importance for asteroseismic studies. We also briefly recall the impact of unknown structural quantities such as the mass and the radius of the star on structural inversion results. We then explain how kernels for new structural variables can be derived using two methods, one suited to asteroseismic targets, the other to helioseismic targets. For this second method, we present a new structural pair, namely thee(/i>i,Y)/span>< /i>esults. &ha numerical tests we carry out allow us to disentangle the impact of various uncertainties in stellar models on the verification of the linear integral relations. We show the importance of metallicity, the impact of the equation of state, extra-mixing, and inaccuracies in the microphysics on the verification of these relations. We also discuss the limitations of the method of conjugated functions due to the lack of extremely precise determinations of masses or radii in the asteroseismic context."/sp siv class="wkord" >/> /pan>class="iaold" /div> ddiv> dp /i>©ESO, 2017"

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